The Flyers were trailing 3-1 midway through the second when the Jets drew a pair of penalties and Claude Giroux began Philadelphia's comeback with a 5-on-3 power-play goal.
Brayden Schenn got the equalizer -- his second tally of the game -- on another man-advantage for the Flyers 6:18 into the third.
Simmonds scored the go-ahead goal less than 3 minutes later, with Winnipeg's Evander Kane serving a double-minor penalty, and the Flyers pulled out their third win in four games.
Simmonds added an assist, Schenn finished with two goals with an assist and Jakub Voracek had three assists.
Ilya Bryzgalov turned aside 34-of-37 shots to earn the victory.